Is it possible for a pion to decay into a proton and a photon?

[Kenai]

Hey guys,
I was wondering if this reactions is possible:

\pi^{+} + n \rightarrow p + \gamma

(Assuming there is enough energy in the initial state to make the reaction go)

If not, what law is violated?

Lepton and baryon numbers are ok... also angular momentum, so I guess it's possible, but still... I can't figure out how to draw the feynman diagram, since there is a total of 5 quarks in the initial state (u,\bar{d}... d,d,u) and there is just 3 in the final state (u,u,d and gamma).

At first, I was thinking in merging d and \bar{d} into a photon , but just 1 photon would violate the momentum conservation law...

Any ideas?

Thanks

 

[daschaich]

I can't figure out how to draw the feynman diagram

I would attach gluon(s) to the quark lines, and have a quark radiate a photon.

 

[Kenai]

I would attach gluon(s) to the quark lines, and have a quark radiate a photon.

Ok, a gluon can be attached into d, \bar{d}

But then I would have an excited system with:

d \bar{d} \rightarrow \it{g}

Which is the problem, since I would already have the u u d configuration necessary for the proton in the final state, and the gamma can come from radiation from a quark as you said.

I'm using now the W boson to interact with one of the down quarks producing an up quark, I guest that would be possible. What do you guys think?

 

[daschaich]

All of your hadrons are bound states, and have tons of glue floating around inside them. I'm coming from a lattice QCD perspective, where we don't even bother drawing the gluons; we just use "quark-line diagrams" (and compute the path integral nonperturbatively...).

At any rate, two quick comments:

1) Your diagram basically has pi^+ converting into a W^+. This is going to be way off mass-shell, and also introduces two weak vertexes. I suspect it is negligible.

2) Isn't this process just pion photo-production "in reverse"? There should be lots of relevant literature about gamma-p interactions. They may invoke some "hadronization" for the pion and nucleon final states, in lieu of dealing with the glue.

 

[Kenai]

i got it! =)

I just turned d dbar into a gluon and made it interact with another quark, producing a photon as in the Compton Scattering pointed here:
http://www-e706.fnal.gov/gifs/feynman-dp-color.jpeg

q \it{g} \rightarrow q \gamma

:)

 

[Parlyne]

1) Your diagram basically has pi^+ converting into a W^+. This is going to be way off mass-shell, and also introduces two weak vertexes. I suspect it is negligible.

I would guess that the helicity problem with that is worse than the mass shell suppression.